Steam-turbine rotor and method of avoiding wave phenomena therein



Jul 29,1924. 1,502,903

w. CAMPBELL STEAM vTURBINE ROTOR AND METHOD OF :WUEING WAVE 'FHENO'MENA THEREIN 'Invntou:

Wilfred Campbell,

- v W QM f jfI-Iis Attorney,

July 29, 1924.

W. CAMPBEL L STEAM TURBINE ROTOR AND METHOD OF AVOIDING WAVE PHENOMENA THEREIN Filed Feb. 27 -1923 14 Sheets$heet 3 1; IIIIIIIIIIII I Inventor Wilfred Campbell His Attor ne y. I

July 29 1924.

1502.903 w. CAMPBELL V STEAM TURBINE ROTOR AND METHOD OF AVOIDING WAVE PHENOMENA THEREZIN Filed Feb. 27. 1923 14 Shets-Sheet 4 1 Inventor Wilfived fiampbe ll.

His Attorney.

Jul 29, 1924. 1.502.903

W. CAMPBELL STEAM TURBINE ROTOfi AND METHOD OF AVOIDING WAVE PHENOMENA THEREIN File e 27. 1923 14 Sheets-Sheet 5 Fig.7.

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His Attorney v Wilfred Campbell,

July 29 1924. 1,502,903

W. CAMPBELL STEAM TURBINE ROTOR AND METHOD OF AVOIDING WAVE PHENOMENA THEREIN Filed Feb. 27. '1923 14 Sheets-Sheet 6 5 Inventor Wilfred Campbell,

His Attorhey.

' July 29, 1924. 1502.903

W. CAMPBELL STEAM TURBINE ROTOR AND METHOD OF AVOIDING WAVE PHENOMENA THEREIN ile e 27. 1923. 14 Sheets-Sheet '7 Inventor Wilfred Campbell,

His Attorney July 29', 1924. 1,502,903

w. CAMPBELL 1 STEAM TURBINE ROTOR AND METHOD OF AVOIDING WAVE PHENOMENA THEREIN Filed Feb. 27 1923 14 Sheets-Sheet 8 Fig.

His Attorney July 29. 1924. 1,502,903

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July 29 1924. 1,502,903

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Inventor His Attorney.

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July 29 1924. 1,502,903

W. CAMPBELL STEAM TURBINE ROTOR AND METHOD OF AVOIDING WAVE'PHENGMENA THEREIN Filed Feb. '27. 192: 14 Sheets-Sheet 11 Fig. 25.

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' Inventor Wilfred Campbell His Attorney July 29 1924.

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July 29, i924. 1,502,903

- W. CAMPBELL STEAM TURBINE ROTOR AND METHOD OF AVOIDING WAVE PHENOMENA THEREIN Filed Feb. 27. 1923 14 Sheets-Sheet 14 m Inventor Wilfred Campbell,

His Attofl ney,

Patented July 29, 1924.

UNITED STATES-"1 WILFRED CAMPBELL, OF SGHENECTADY, NEW YORK, ASSIGNOR T GENERAL ELECTRIC COMPANY, A CORPORATION OF NEW YORK.

Application filed February 27, 1923. Serial No.- 621,655.

To all whom may concern:

Be it' known that I, WILFRED CAMPBELL,

a subject of the King of Great'Britain, residlng at Schenectady, county of Schenec-.

5 tady, State of New. York, have invented certain new and useful Improvements in Steam-Turbine Rotors and -Methods of Avoiding Wave Phenomena Therein, of

which the following is a specification.

In the natural course of development of the multistage steam turbine, especially those of the impulse type, and as turbine wheelswere made larger and larger, and

ran at higher and higher peripheral speeds,

breakage of the turbine wheels and breakage of the buckets frequently occurred, which resulted in many cases in actual wrecking of the turbine as a whole. The underlying cause of these troubles has heretofore not been discovered, and accidents in the operation of steam turbines have become more and more frequent, and more and more serious.

I have discovered that the breakages in steam turbine wheels and buckets are due primarily to the development in the wheels of actual wave motions which travel in the wheels. These waves travel in a wheel at speeds depending upon any one of a number of natural periods of vibration. of the wheel itself. I have found that when these waves have a direction of trayel inthe wheel opposite to that of the direction of rotation, dangerous conditions develop if the backward speed of the wave is equal to the forward speed of rotation f the wheel. Under such conditions a backward traveling wave becomes stationary in space, and the amplitude of such a wavemay therefore become very large through the application to the Wheel of any force stationary in spa-co tending to deflect the Wheelin an axial direction. The repeated bending stresses produced in the wheel by traveling waves finally lead to fatigue fractures in the wheel structure.

As will beset forth more in detail hereinafter, I have devised methods whereby the wave phenomena produced in turbine wheels may be predetermined and, by'suitable designing and proportioning of the wheel, controlled so as to remove a serious menace heretofore present in the operation of tur- I made up of individual wheels, all at which,

by suitable predetermination or tuning, are rendered free fromv objectionable wave phenomena'at speeds in the immediate vicinity of the normal operating speed of the rotor. The tendency in any wheel of the rotor to produce" objectionable wave phe nomena at speeds in the neighborhood of the operating speed is ascertained and is definitely controlled so as not to come into normal operating. speed of the rotor by less than certain predetermined limits.

a wheel, and to predict the speeds-at which such phenomena will develop; whereby such modification or redesigning or proportioning of the wheel structure as may be necessary, can be performed so as to shift such dangerous critical speeds as may occur, away from dangerous proximity to the normal operating speed of the rotor.

My invention itself will be better understood by reference to the accompanying drawings taken in connection with the following specification.

Fig. 1 is a representation, taken from an actual photograph, of a 17 stage 30,000 kilo: wattturbo-alternaton built in accordance with my invention, with the turbo-cylinder cover removed to expose to view the turbine wheels of the rotor. In this figure'the turbine shaft is indicated at 1; the first or high pressure wheel of the series of wheels on the rotor is indicated at 2; and the last or 17th stage wheel at 3. The alternator driven by the turbine is indicated at 4:. The extremity of the lower half of the diaphra In between turbine wheels is indicated, for example, at 5.

. Fig. 2 1s a view of a turbine rotor showing the remains of a wheel out ofwhich a large section has been broken.

Fig. 3 is a view of he turbine wheel out operation at any speed differing from the of which a section, extending only slightly into the web of the wheel, has been broken. Fig. 4 is a view of a turbine wheel in which the breaks have extended only to the buckets themselves; while Fig. 5 is aview-on an enlarged scale of a broken portion of the wheel shown in Fi 6 is a view of the assembled remains of a roken-turbine wheel.

Fig. 7 represents a diaphragm in ured by rubbing.

Figs. 8, 9, 10 and 11 represent various types of nodal vibrations in aturbine wheel.

Fig. 12 is a view of a wheel testing machine; while Figs. 13, 14 and 15 are details of parts thereof.

Fig. 16 is a diagram of circuits.

Figs. 17 to 21 inclusive are representations of typical oscillograph records.

Figs. 22 and 23 are diagrams showing relations between wheel speeds and wheel frequencies.

Figs. 24 and 25 are typical diagrams representing the A critical speeds for various wheels of turbine rotors in which some of the critical speeds occur in dangerous proximity to the running or operating speed.

Figs. 26 and 27 are diagrams representing the relation of critical speeds to the operating speed of various wheels of two turbine rotors in which no critical speed occurs within dangerous proximity to the operatin speed.

igs. 28 to 34 inclusive are partial sectional views of turbine wheels representing the removal of material from portions of a wheel for purposes of tuning.

. Figs. 35, 36, 37, 38, 39 and 40 are detailed gielviys of a device for vibrating a turbine While the development of the turbine art dates back many years, only about one decade has passed since troubles began to be experienced with bucket wheels of steam turbine rotors, especially of the impulsetype, due to cracking or actual breakage of the wheel disks or of the buckets themselves. In the .early stages of the development, these troubles were comparatively infrequent, and they came into prominence only as turbines of larger and larger sizes were built. In many of these large turbines the turbine disks were actually broken and large sections of the wheels themselves were thrown off so as, not only to wreck the turbine, but to damage neighboring apparatus, and, in many cases, cause loss of life.

Fig. 2 of the drawings is a representation of a fracture of a turbine disk'extending deep down into the disk itself, showing that a large section of the wheel, along with the buckets mounted thereon, had been driven off. It is to be noted that the part of the fracture indicated at 6 is of a peculiar feathery appearance, which cannot be well shown in the drawing, but which is always associated with breaks due to fatigue strains. The outline of this part follows roughly the arc, of a circle of relatively small radius. The outer sections 7' and 8 of the break bear less marked evidences of fatigue strains. The significance of this kind of a break will later be pointed out.

Since the weight of such a broken-out section of the wheel, as indicated in Fig. 2, may amount to from 50 to 250 pounds, and since the peripheral velocity of the wheel may be not greatly different from the muzzle velocity of a cannon ball, it can readily be seen what enormous energy is released by a break of this character.

Fig. 3 is a representation of a portion of a'large steam turbine after a break of the general character described had occurred. It will be seen that the casing or shell of the turbine has been wrecked, as indicated at 9. In this case the broken-out section of the wheel extends only slightly into the body of the wheel disk as at 10. The character of the break at 10, which cannot be well shown in a drawing, again indicates a fatigue rupture. It is to be noted that the break extends through holes 11 and 12.

In Fig. 4 aturbine wheel disk is shown at 13, provided with a single peripheral row of buckets 14. The view of this picture-was taken from an actual photograph and represents the turbine rotor mounted upon a shaft and carried by a temporary support 15. It will be observed that nu-' merous buckets have been broken out of the wheel, as indicated by the vacant places such as 16, 17 and the like. Fig. 5 shows an enlarged view of the .broken buckets corresponding to :the section marked 17 in Fig. 4. 'Thenature of the fractures where thebuckets were broken, as for example, at 18 and 19 indicates, as before, breaks due to fatigue action. It will also be noted that at 20 a bucket has been broken out and that the tenon 21 still remains in the bucket cover 22. As will be pointed out hereinafter, the traveling wave produced in this turbine wheel resulted in a shearing off of the tenon, not only in this case, 21, but in the case of the tenon the remains of which are indicated at 23. It is to be observed that the fatigue breaks, in..the instances shown in Fig. 4, and in detail in Fig. 5, extend through the buckets only and do not extend into the wheel disk at all. In other words, the radial depth at which the fatigue fractures occurred in the wheel shown in Fig. 4 is still less than that in the wheel shown in Fig. 3. Along with the fracture of the turbine buckets themselves it will of course be noted that the shroudbands or bucket covers have been driven off at various places in the periphery of the wheel as, for example, at points 16 and 17, already indicated. i Fig.6 is a view showing parts of a tur/ bine wheel picked up afteran accident and pieced together as shown; It will be noted that in this case, as well as in Fig. 3, an outline of the ruptured sections passes through certain balancing or steam 'equaliz-. ing holes indicated at 24 and25. Furthermore, it will be observed in this figure at 26, that by some kind ofrubbing action the buckets had in places actually been melted down by the generation of intense heat.

Another manifestation frequently met with is illustrated by Fig. 7. This figure is a representation of a stationary diaphragm which, in the turbine itself,.- lies between two turbinewheels, as is well understood in the art. The diaphragm is made in two halves along a horizontal dividing plane as at 27, and is assembled around the shaft with suitable packings to prevent escape of steam through the opening for the shaft. The diaphragm has a central solid web 28 and an outer row of nozzles 29. It will be apparent from the drawings that those nozzles in the diametrically opposite regions marked 30 and 31 have apparently been scraped. or rubbed by some rough body, while in other portions of the diaphragm no such rubbing has occurred. The signifi cance of this will be hereinafter pointed out. a

An enormous. amount of investigation has been made by Workers in this art in order to solve the difiiculties arising from breakages and similar troubles of the general nature already described. Explanations of many kinds have been made to account for these difficulties. It might be supposed that centrifugal forces would account for the more serious breakages. Careful calculation, however, of the stresses involved and of the strength of material of wheelsv has shown,that a margin of safety against centrifugal force exists so ample that such an explanation is'by no means adequate.

In the case of large turbine disks it was at one time supposed that inequalities-of heating of the disk, the disk being hotter near the periphery than near the center, might cause the disk to buckle into a sort of wavy form around the periphery, wherebycertain portions ,of the disk would be apt to rub against adjacent diaphragms or other parts of the turbine structure. This explanation would not, however, account for the rubbing of a diaphragm in equi-spaced areas as at 30 and 31. in Fig. 7.

Shortly after difficulties due to rubbingand breakage of the steam turbine wheels began to appear, it was suggested by Prof. Stodola, "a recognized; authority 'on steam turbines, in an article entitled (when translated), On thevibration of rotating turbine wheels, published in the Schweizeri- /sche Bauzeitung, May 2, 1914, page 251, that the wheel disks themselves were set into vibration and that these vibrations could become so large that the wheel rim begins tov rub against stationary parts, and they immediately become red hot, so that very dangerous conditions are created.

Stodola thereupon made a complicated mathematical investigation of a purely theoretical nature in order to account for the difliculties observed, and he concluded that the vibrations occuring in the turbine disks were nodal in character and might be expected to become dangerous due to resonance with axial vibrations caused by the partial peripheral admission of steam to the turbine disk, or to certain mistakes of construction such, for example, as when the steam hits the wheel rim periodically at certain places. But this attemped explanation applies, if at all, only to the first stage or wheel, whereas most of the difficulties which have arisen of the character described have occurred in the larger wheels of the rotor, in the lower pressure stages. Stodola proposed no practical remedy. The breakage difliculties in steam turbine rotors not only continued but became increasingly serious as larger and larger turbines were built and put vinto op: 'eration. Moreover, the troubles occurred in turbines having full peripheral admission of steam instead of partial peripheral admission. i

A list of some of the accidents, together with other details, which have occured in the operation of large steamturbines is set forth in a paper by Baumann on Some recent developments in large steam turbine practice published in the Journal of the Institution of Electrical Engineers (London) vol. 59, 1921, pags;565 to 663. After describing the difficulties. Which had been experienced in the operation of steam turbine wheels, especially of large diameter,

due in some manner to vibration of the disks themselves, the author states (page 620) that Owing to the lack of satisfactory ro' posals to overcome the difficulties w ich, have been experienced, due directly or indirectly to the use of high peripheral speeds, the tendency towards the employment of such high peripheral speed has received a definite check, and a more conservative policy at the present time is more likely to produce satisfactory results. It is therefore essential that the rigidity of the disks should be such as to preclude their vibration.

In'fthe discussion of this paper Mr, S. E. Fedden proposed (page630) as a remedy for these difiiculties, that the wheels or rotors should be periodically removed from the turbine and rebuilt so as thereby to avoid disastrous results due to fatigue effects following recurrent stresses. He states:

I presume that after a certain amount of time it will be necessary to take the rotor out and completely reblade it, in order to be on thesafe side and prevent a catastrophe.

And he thereafter says,

There must besomething wrong in the design and the manufacture of these turbines to cause such a number of breakages. There is little doubt that turbine makers will put their heads together and learn how to get over these difliculties.

Mr. Kaula stated (page 633) In the meantime the main obstacles in the way of the large single-flow design seem to be the difiiculty of obtaining a disk of consistently reliable material throughout, coupled with disk vibration, about which little is. known. The latter problem is very much akin to that of critical speeds (meaning critical shaft speeds) which was being attacked in 1912 when the author read his previous paper.

Again Mr. Kaula states (page 634) If further experience proves that various forms of vibrations which may be transmitted to the disk in one form or another are apt to produce resonance vibrations of adangerous order in the disk, it will be necessary to "determine two factors; first, what nature of vibrations causes such effects, second, what is the period of these vibrations? If these two factors can be predetermined it should be a comparatively simple matter to insure that the natural periods of all disks are well removed from the periods of the vibrations in question.

Dr. Stodola himself contributed a written discussion of the same paper (page 637) but he was silent as to any remedies for the difiiculties pointed out.

Baumann (page 638) proposed as a solution that the use of large disks be avoided, and he further recommended (page 642) that such disks as are employed shall not vibrate under any conditions, and that theydshall be run at moderate peripheral s ee s;

However, to lessen the diameter of wheel disks and to decrease their normal running speed, all for the purpose of avoiding difliculties due to disk vibrations or wave phenomena, would be a step in the wrong direction in the'development of the steam turbine for modern uses. It is well to bear in mind that the application of the steam turbine to the'driving of electric generators was one of the most important single steps in the development of the electrical industry. During the last decade the size of turbine generator units has steadily increased until now a 35,000 kilowatt turbine is a familiar unit. Largely by this increase in size, as well as by the great increase in peripheral speeds, the electrical output per unit of steam of these present day large turbine generators is approximately twice the electrical output, for the same quantity of steam, of the best machines built in 1903.

This enormous increase in efiiciency' and in output is a matter .of the utmost practical importance. It is not too much to say that the displacement of the steam engine by the modern large turbo-alternator, with the corresponding reduction in capital cost of the complete generating station, coupled with the corresponding saving in operating costs, has made possible the modern electric power plant. Hence, except-possibly in' some special case, no proposal for. obviating diificulties arising from wave phenomena in turbine disks or wheels can be considered which might have the effect of reducing the output or efficiency of the turbine. I

As a result of-my investigations I have found that it is not at all necessary, in order to obviate difilculties due to wave phenomena in the turbine wheel or buckets, that the wheel should be so stiffened and its peripheral speed reduced as to avoid all vibration whatever. On the contrary, turbine wheels are now regularly produced in accordance with my invention which, although susceptible to wave phenomena at certain speeds, in the neighborhood of the normal operating'speed of the wheel, yet are entirely free from this difficulty at the normal operating speed and at all speeds which do not differ from the normal'operating speed by more than predetermined safe margins.

The rotational speeds of turbine wheels at which wave phenomena due to radial nodal conditions may develop markedly I refer to herein as critical speeds. Such critical speeds occur in turbine wheels whether such wheels are in a condition of practically perfect balance or not-and are a function of the mass and of the stiffness or natural resiliency ofthe wheels modified by centrifugal force, as herein explained. These critical speeds are to be distinguished sharply from critical speeds of shafts which arise from static or dynamic unbalancing of the rotating shaft. Critical shaft speeds are thoroughly understood, but they have nothing in common with critical speeds ofthe' nature herein contemplated. v

For each turbine wheel there is a considerable number of. nodal critical speeds.

.Thus, for example, there is a critical speedcorresponding to the tendency of the wheel to vibrate in four radial nodes, and further critical speeds identified by vibrational tendencies corresponding to six nodes, eight nodes, ten nodes, twelv nodes and so on; for each of these tendeiibies there is a corresponding critical speed. It will be evident, therefore, that in view of the multi-' plicity of critical speeds at which wave phenomena may be set up in a turbine disk, the proposal merely to change. the degree of stifi'ness of the turbine wheel would be aslieved that by replacing the wheel by an-v other wheel of heavier construction the difficulty might be avoided. ingly done, but the new wheel, "within a very short time after the turbine was put.

in operation, again developed trouble of a character worse-than the original trouble.

From my present discoveries I now know that, by this alteration in proportions,' the various natural periods of vibration of the new wheel had been so displaced, as compared with those of the old wheel, as to bring the corresponding critical point of the new wheel away from. dangerous proximity to the operating speed, but at the same time so as to bring a different critical point, corresponding to a difi'erent number'of nodes, intoddangerous relation to the operating spee I have discovered that the wave phenomena in turbine wheels can be freed fromdanger by an exact predetermination of the critical speeds of the wheels, and by such adjustment or modification of the wheels themselves, in some cases referred to herein as tuning, as to bring dangerous critical speeds by a safe margin outof the immediate region of the normal operating speed of the turbine. V f

In accordance with my invention, I do not aim to avoid the occurrence of criticalspeed tendencies inturbine wheels, but to avoid any such tendencies at speeds dangerously close to the normal operating speed. In

' turbines of sufiiciently small size, and'which do not embody my invention, the diameters of the wheels are necessarily small, and the wheels themselves are relatively Hence, althoug'hthese wheels may rotate atrigid.

high speed, nevertheless the normal operat-' ing speeds are far below the neighborhood of the frequencies at which the wheels would tend to produce nodal. wavefphenomena.

The critical s peeds, the refore,' being far abovethe normal operating speeds; could never give difficulty due to wave phenomena.

By the methods which I have. devised steam turbine rotors are produced inwhich, 7 by predetermination, all of the wheels, without exception, are made free from objectionable wave phenomena within certain is was accordnormal operating speed. The rotors, hoW-.

ever, arecharacterized by the factthat they have critical speeds in one or more of the wheels'in the neighborhood of the operating speed, but safely removed therefrom. In some cases there may be some critical speeds above and some below the operating speed, and in other cases, as is preferable, all of the critical speeds lie above the normal operating speed.

Wherever herein I'refer to critical speeds of a turbine wheel or rotor as being in the neighborhood 'of its normal operating speed, I refer to such a degree of proximity that the ordinary variations in design and irregularities of" manufacture of such turbine wheels or rotors might be expected, in some cases at least, to result in wheels having certain critical speeeds in dangerous proximity to the operating speed. Actual "experience leads me to the conclusion that if a turbinev wheel has a critical speed dif-' fering from the normal operating speed by not materially more than 30 per cent of the normaloperating speed, then the degree of proximity of the critical speed to the operating speed is such that precaution as herein explained must be observed in the manufacture of such wheels, and for that reason I may refer tosuch critical speeds turbine rotor differs therefrom by materially more than 30 per cent, my experience shows that ordinary variations in design and irregularities of manufacture of that t pe of wheel are not likely to'resultin a wheel having a critical speed substantially closer to the normal operating speed than the safe limits hereinafter specified and such critical *speed I consider as not being in the neighborhood of the operating speed. Those turbinerotors having all of their wheels, without exception, with critical speeds differing from the normal operating speed by materially more than 30 per cent, are therefore not of a type requiring the practice of my invention.

The vibrational tendencies of turbine wheels which lead to the production of wave phenomena maybe considered first in, the relations which present themselves. when 'fthe wheel is at rest. a Figs. Sand 9 1:0

and llare representations, taken rrp etual photographs, of a turbine wheel jarrest. I In eachcase paper' has been: spread over the bucket area'of'the wheel indicated by the ring-shaped areas 32 and 33 and 3i and 35. In Fig. 10, the paper is represented as being cut away at 36 in order to show the bucket area 37 immediately beneath. I

In each instance shown in Figs. 8 to 11, an electromagnet 38 ismounted on a suitable support, not shown, in proximity to the turbine wheel. When an alternating current of any desired frequency is sent through this magnet, the current being obtained from a suitable source, such as a varlable speed motor generator set, the magnet exerts a periodic pull upon the rim of electromagnet is then gradually varied until the coal shows a tendency to collect in the form of certain geometrical figures on the surface of the wheel. When the frequency of the magnetic pull in the magnet happens to coincide with some natural period of vibration of the disk, the coal granules produce ageometrical figure having either two or four or six or eight or some higher number of cusps or points joined together by intervening loops so as'to make a sort of a scallop. The outlines of these geometrical figures are formed of collections of coal granules which indicate points where the wheelis at rest, whereas the areas or ventral segments of the wheel, from which coal granules have been shaken free, correspond to those parts in which vibration has oc curred. Thus around the wheel shown in various conditions in Figs.- 8 to 11, are con figurations or coal granule fi' res showing that, in the respective cases; t ere were two points 39 and 40 in Fig. 8' at which there was substantially no vibration, while in Fig. 9 there were four corresponding points '41 ,to 44; in Fig. 10, six corresponding points 45 to 50; and in Fig. 11, eight corresponding points 51 to 58. These points may be designated as radial nodes.

Fig. 8 therefore represents a vibrational I tendency corresponding to two nodes; Fig. .9 a vibrational tendency corresponding to four nodes; Fig. 10 a vibrational tendency corresponding to six nodes; and Fig. 11 a vlbrational tendency corresponding to ei ht nodes. -All of these figures .re resent .di erent conditions of the same i entical wheel, and show clearly that such a wheel may vibrate in two nodes or four nodes or six nodes or eight nodes according to the frequency of vibration imposed upon the wheel by the alternating current magnet or other vibrating forces. It isonly when the externally applied vibrating force comes into speeds of rotation at which resonance effects tend to be produced in the wheel itself the vibrating nodal sections of the wheel do not remain fixed in the wheel, as exhibited in Figs. 8 to 11, but give rise to nodal traveling waves of considerable magnitude. As

each point in the wheel rim is periodically displaced from side to side of the wheel the disturbance is transmitted around the wheel itself as a wave motion. That motion is increased in amplitude by any applied force transmitted from the outside of the wheel in resonance with, or approximately in resonance with series of waves corresponding to some natural period of vibration which would tend to roduce nodes. In practice it has been foun that for each of the nodal critical speeds there is a wave traveling backward in the wheel at the same speed as the forward travel of the wheel, whereby the wave becomes stationary in space. Being thus stationary in space, any force' or im pulse imparted to the wheel from points outside the wheel will act continually to increaseor sustain the amplitude of the wheel deflection. This is a dangerous condition of resonance.

' At the same time that such stationary waves are produced there may be a forward traveling wave, due perhaps to reflection from the backward traveling wave caused by irregularities in the wheel structure, but it is found in practice that such a wave is generally of negligible amplitude.

en a backward traveling wave has been initiated in a turbine wheel some small portion of the reaction steam energy is absorbed in building up and maintaining this typeof wave. At the same time, the same reactive steam giiergy will tend to dampen the for ward wave when onc initiated. One articular wheel of large diameter requlred only about 80 watts of energy in causing and maintaining a vibration of dangerous amplitude. In service about 6000 kw. of steam energy entered this sta e of the turbine, about 2000 kw. of energy eing rejected as residual. The feathering action of the buckets due to a backward wave travel causes a pulsating variation in the axial component of the reactive steam energy which is in direction and time the same as the natural period of the wheel itself; for a forward wave the pulsation would be in time but opposite in direction to the natural vibrat on period and, therefore, is dampened b 

